scholarly journals Grover on PIPO

Electronics ◽  
2021 ◽  
Vol 10 (10) ◽  
pp. 1194
Author(s):  
Kyungbae Jang ◽  
Gyeongju Song ◽  
Hyeokdong Kwon ◽  
Siwoo Uhm ◽  
Hyunji Kim ◽  
...  
Keyword(s):  
Block Cipher ◽  
Search Algorithm ◽  
Quantum Algorithms ◽  
Optimization Techniques ◽  
Quantum Circuits ◽  
Brute Force ◽  
Grover Search ◽  
Quantum Simulator ◽  
Compact Design ◽  
Grover Search Algorithm

The emergence of quantum computers is threatening the security of cryptography through various quantum algorithms. Among them, the Grover search algorithm is known to be efficient in accelerating brute force attacks on block cipher algorithms. To utilize the Grover’s algorithm for brute force attacks, block ciphers must be implemented in quantum circuits. In this paper, we present optimized quantum circuits of the SPN (Substitution Permutation Network) structured lightweight block cipher, namely the PIPO block cipher. In particular, the compact design of quantum circuits for the 8-bit Sbox is investigated. These optimization techniques are used to implement other cryptographic operations as quantum circuits. Finally, we evaluate quantum resources of Grover search algorithm for the PIPO block cipher in ProejctQ, a quantum simulator provided by IBM.

scholarly journals Efficient Implementation of PRESENT and GIFT on Quantum Computers

2021 ◽  
Vol 11 (11) ◽  
pp. 4776
Author(s):  
Kyungbae Jang ◽  
Gyeongju Song ◽  
Hyunjun Kim ◽  
Hyeokdong Kwon ◽  
Hyunji Kim ◽  
...  
Keyword(s):  
Block Cipher ◽  
Search Algorithm ◽  
Block Ciphers ◽  
Quantum Circuits ◽  
Security Level ◽  
Symmetric Key ◽  
Grover Search ◽  
Target Block ◽  
Symmetric Key Cryptography ◽  
Grover Search Algorithm

Grover search algorithm is the most representative quantum attack method that threatens the security of symmetric key cryptography. If the Grover search algorithm is applied to symmetric key cryptography, the security level of target symmetric key cryptography can be lowered from n-bit to n2-bit. When applying Grover’s search algorithm to the block cipher that is the target of potential quantum attacks, the target block cipher must be implemented as quantum circuits. Starting with the AES block cipher, a number of works have been conducted to optimize and implement target block ciphers into quantum circuits. Recently, many studies have been published to implement lightweight block ciphers as quantum circuits. In this paper, we present optimal quantum circuit designs of symmetric key cryptography, including PRESENT and GIFT block ciphers. The proposed method optimized PRESENT and GIFT block ciphers by minimizing qubits, quantum gates, and circuit depth. We compare proposed PRESENT and GIFT quantum circuits with other results of lightweight block cipher implementations in quantum circuits. Finally, quantum resources of PRESENT and GIFT block ciphers required for the oracle of the Grover search algorithm were estimated.

scholarly journals Grover on Korean Block Ciphers

2020 ◽  
Vol 10 (18) ◽  
pp. 6407
Author(s):  
Kyoungbae Jang ◽  
Seungju Choi ◽  
Hyeokdong Kwon ◽  
Hyunji Kim ◽  
Jaehoon Park ◽  
...  
Keyword(s):  
Search Algorithm ◽  
Quantum Circuit ◽  
Block Ciphers ◽  
Research Area ◽  
Quantum Circuits ◽  
Security Level ◽  
Toffoli Gate ◽  
Grover Search ◽  
Target Block ◽  
Grover Search Algorithm

The Grover search algorithm reduces the security level of symmetric key cryptography with n-bit security level to O(2n/2). In order to evaluate the Grover search algorithm, the target block cipher should be efficiently implemented in quantum circuits. Recently, many research works evaluated required quantum resources of AES block ciphers by optimizing the expensive substitute layer. However, few works were devoted to the lightweight block ciphers, even though it is an active research area, nowadays. In this paper, we present optimized implementations of every Korean made lightweight block ciphers for quantum computers, which include HIGHT, CHAM, and LEA, and NSA made lightweight block ciphers, namely SPECK. Primitive operations for block ciphers, including addition, rotation, and exclusive-or, are finely optimized to achieve the optimal quantum circuit, in terms of qubits, Toffoli gate, CNOT gate, and X gate. To the best of our knowledge, this is the first implementation of ARX-based Korean lightweight block ciphers in quantum circuits.

Entanglement in the Grover search algorithm

2005 ◽  
Vol 345 (4-6) ◽  
pp. 265-272 ◽  
Author(s):  
Yiyuan Fang ◽  
Dagomir Kaszlikowski ◽  
Chunming Chin ◽  
Ken Tay ◽  
L.C. Kwek ◽  
...  
Keyword(s):  
Search Algorithm ◽  
Grover Search ◽  
Grover Search Algorithm

scholarly journals Quantum Image Steganography Protocol Based on Quantum Image Expansion and Grover Search Algorithm

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 50849-50857 ◽  
Author(s):  
Zhiguo Qu ◽  
Zhengyan Li ◽  
Gang Xu ◽  
Shengyao Wu ◽  
Xiaojun Wang
Keyword(s):  
Search Algorithm ◽  
Image Steganography ◽  
Quantum Image ◽  
Grover Search ◽  
Quantum Image Steganography ◽  
Grover Search Algorithm ◽  
Image Expansion

Quantum-based algorithm and circuit design for bounded Knapsack optimization problem

2020 ◽  
Vol 20 (9&10) ◽  
pp. 766-786
Author(s):  
Wenjun Hou ◽  
Marek Perkowski
Keyword(s):  
Circuit Design ◽  
Knapsack Problem ◽  
Decision Problem ◽  
Optimization Problem ◽  
Quantum Algorithm ◽  
Quantum Circuits ◽  
Local Quantum ◽  
Speed Up ◽  
Grover Search ◽  
Quantum Simulator

The Knapsack Problem is a prominent problem that is used in resource allocation and cryptography. This paper presents an oracle and a circuit design that verifies solutions to the decision problem form of the Bounded Knapsack Problem. This oracle can be used by Grover Search to solve the optimization problem form of the Bounded Knapsack Problem. This algorithm leverages the quadratic speed-up offered by Grover Search to achieve a quantum algorithm for the Knapsack Problem that shows improvement with regard to classical algorithms. The quantum circuits were designed using the Microsoft Q# Programming Language and verified on its local quantum simulator. The paper also provides analyses of the complexity and gate cost of the proposed oracle. The work in this paper is the first such proposed method for the Knapsack Optimization Problem.

scholarly journals Quantum Circuit Synthesis Using Projective Simulation

2021 ◽  
Vol 24 (67) ◽  
pp. 90-101
Author(s):  
Otto Menegasso Pires ◽  
Eduardo Inacio Duzzioni ◽  
Jerusa Marchi ◽  
Rafael De Santiago
Keyword(s):  
Quantum Computing ◽  
Quantum Algorithms ◽  
Quantum Circuit ◽  
Optimization Techniques ◽  
Error Tolerance ◽  
Quantum Circuits ◽  
Quantum Decoherence ◽  
Circuit Synthesis ◽  
Circuit Optimization ◽  
Learning Technique

Quantum Computing has been evolving in the last years. Although nowadays quantum algorithms performance has shown superior to their classical counterparts, quantum decoherence and additional auxiliary qubits needed for error tolerance routines have been huge barriers for quantum algorithms efficient use.These restrictions lead us to search for ways to minimize algorithms costs, i.e the number of quantum logical gates and the depth of the circuit. For this, quantum circuit synthesis and quantum circuit optimization techniques are explored.We studied the viability of using Projective Simulation, a reinforcement learning technique, to tackle the problem of quantum circuit synthesis. The agent had the task of creating quantum circuits up to 5 qubits. Our simulations demonstrated that the agent had a good performance but its capacity for learning new circuits decreased as the number of qubits increased.

scholarly journals Search via quantum walks with intermediate measurements

2015 ◽  
Vol 29 (19) ◽  
pp. 1550127
Author(s):  
Efrain Buksman ◽  
André L. Fonseca de Oliveira ◽  
Jesús García López de Lacalle
Keyword(s):  
Close Relationships ◽  
Search Algorithm ◽  
Quantum Algorithms ◽  
Quantum Walks ◽  
Quantum Search ◽  
Brute Force ◽  
Correlation Measure ◽  
Quantum Search Algorithm ◽  
Control Qubit ◽  
Modified Algorithm

A modification of Tulsi's quantum search algorithm with intermediate measurements of the control qubit is presented. In order to analyze the effect of measurements in quantum searches, a different choice of the angular parameter is used. The study is performed for several values of time lapses between measurements, finding close relationships between probabilities and correlations (mutual information and cumulative correlation measure). The order of this modified algorithm is estimated, showing that for some time lapses the performance is improved, and becomes of order O(N) (classical brute-force search) when measurements are taken in every step. The results provide a possible way to analyze improvements to other quantum algorithms using one, or more, control qubits.

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